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In the figure, masses m(1), m(2) and M a...

In the figure, masses `m_(1), m_(2)` and M are 20kg, 5kg, and 50kg respectively. The coefficient of friction between M and ground is zero. The coefficient of friction between `m_(1)` and M and that between `m_(2)` and ground is 0.3. The pulleys and the strings are massless. The string is perfectly horizontal between `P_(1)` and `m_(1)` also between `P_(2)` and `m_(2)`. The string is perfectly vertical between `P_(1)` and `P_(2)`. An external horizontal force F is applied to the mass M. Let the magnitude of the force of friction between `m_(1)` and M be `f_(1)` and that between `m_(2)` and ground be `f_(2)`. For a particular F it is found that `f_(1) = 2f_(2)`. [Take `g = 10 m/s^(2)`]
(i) Find `f_(1)` in Newton
(ii) Find `f_(2)` in Newton
(iii) Find F in Newton
(iv) Find tension in the string in Newton
(v) Find acceleration of the masses in `m//s^(2)`

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